Mr Lee had an apple 🍎, a papaya 🫚 and a honeydew 🍈. He weighed them in PAIRS: apple + papaya = 730 g, apple + honeydew = 1960 g, honeydew + papaya = 2470 g. What was the mass of the honeydew?
| weighing | mass |
|---|---|
| 🍎 + 🫚 (apple + papaya) | 730 g |
| 🍎 + 🍈 (apple + honeydew) | 1960 g |
| 🍈 + 🫚 (honeydew + papaya) | 2470 g |
Look closely: 🍎 appears twice, 🫚 appears twice, 🍈 appears twice. Adding all three rows counts every fruit's mass exactly twice over.
"apple + papaya" (730 g) is the only weighing with no honeydew in it, so:
is the mass of the honeydew.
The trap: subtracting two of the weighings and hoping. Adding ALL THREE and halving is what turns three pair-weights into the single total — the rest is one subtraction.